Absolute value equations. (English) Zbl 1172.15302
Summary: We investigate existence and nonexistence of solutions for NP-hard equations involving absolute values of variables: \(Ax -| x| = b\), where \(A\) is an arbitrary \(n\times n\) real matrix. By utilizing an equivalence relation to the linear complementarity problem (LCP) we give existence results for this class of absolute value equations (AVEs) as well as a method of solution for special cases. We also give nonexistence results for our AVE using theorems of the alternative and other arguments.
MSC:
| 15A39 | Linear inequalities of matrices |
References:
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